0.01/10.428 *10^-5

asked by guest
on Nov 25, 2024 at 7:40 pm



You asked:

Evaluate the expression: \(\frac{0.01}{10.428} \cdot {10}^{-5}\)

MathBot Answer:

\[\frac{0.01}{10.428} \cdot {10}^{-5} = \frac{1}{104280000} = 0.000000\overline{00958956655159186804756425}\]

\[\begin{aligned}\frac{0.01}{10.428} \cdot {10}^{-5}& = \frac{1}{100} \cdot \frac{1}{10 + \frac{428}{1000}} \cdot \frac{1}{10^{5}}\\& = \frac{1}{100} \cdot \frac{1}{10 + \frac{107}{250}} \cdot \frac{1}{10^{5}}\\& = \frac{1}{100} \cdot \frac{1}{\frac{2607}{250}} \cdot \frac{1}{10^{5}}\\& = \frac{1}{100} \cdot \frac{250}{2607} \cdot \frac{1}{10^{5}}\\& = \frac{1}{100} \cdot \frac{250}{2607} \cdot \frac{1}{100000}\\& = \frac{5}{5214} \cdot \frac{1}{100000}\\& = \frac{1}{104280000}\end{aligned}\]

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